Image clustering with tensor representation
Image clustering with tensor representation
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DOI：
10.1145/1101149.1101169
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发表时间：
2005-11
期刊：
影响因子：
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通讯作者：
Xiaofei He;Deng Cai;Haifeng Liu;Jiawei Han
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文献类型：
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作者：
Xiaofei He;Deng Cai;Haifeng Liu;Jiawei Han
我们考虑图像表示和聚类的问题。传统上，n1 x n2 图像由欧几里得空间 ℝ n1 x n2 中的向量表示。然后将一些学习算法应用于如此高维空间中的这些向量，以进行降维、分类和聚类。然而，图像本质上是一个矩阵，或二阶张量。图像的矢量表示忽略了图像中像素之间的空间关系。在本文中，我们介绍了用于图像分析的张量框架。我们将图像表示为张量空间 Rn1 数学 Rn2 中的点，它是两个向量空间的张量积。基于张量表示，我们提出了一种新颖的图像表示和聚类算法，该算法明确考虑张量空间的流形结构。通过保留数据流形的局部结构，我们可以获得局部等距意义上的最佳数据表示的张量子空间。我们称之为 TensorImage 方法。然后将传统的聚类算法（例如 k-means）应用于张量子空间。我们的算法共享其他技术的许多数据表示和聚类属性，例如局部性保留投影、拉普拉斯特征图和谱聚类，但我们的算法的计算效率更高。实验结果表明了我们算法的效率和有效性。
We consider the problem of image representation and clustering. Traditionally, an n1 x n2 image is represented by a vector in the Euclidean space ℝ n1 x n2. Some learning algorithms are then applied to these vectors in such a high dimensional space for dimensionality reduction, classification, and clustering. However, an image is intrinsically a matrix, or the second order tensor. The vector representation of the images ignores the spatial relationships between the pixels in an image. In this paper, we introduce a tensor framework for image analysis. We represent the images as points in the tensor space Rn1 mathcal Rn2 which is a tensor product of two vector spaces. Based on the tensor representation, we propose a novel image representation and clustering algorithm which explicitly considers the manifold structure of the tensor space. By preserving the local structure of the data manifold, we can obtain a tensor subspace which is optimal for data representation in the sense of local isometry. We call it TensorImage approach. Traditional clustering algorithm such as k-means is then applied in the tensor subspace. Our algorithm shares many of the data representation and clustering properties of other techniques such as Locality Preserving Projections, Laplacian Eigenmaps, and spectral clustering, yet our algorithm is much more computationally efficient. Experimental results show the efficiency and effectiveness of our algorithm.